So, I finished my game a while ago and I decided to replay it on Critical Mode and the game lets you start all over again with your previous Dream Eaters and Trophies. My questions is: should I replace my existing data or start a new game outright (no Dream Eaters or Trophies)?

 

My only worry is that if I erase my data, and since Critical mode is way more difficult, I won't be able to pick up the game anytime because I could get stuck.

I really can't say if you'll get stuck or not. I've played almost every KH game on the highest setting and haven't gotten stuck at one point for too long. Even with your old dream eaters, there will be battles you will have to replay. The only thing is that with your dream eaters, you can get really good commands early in the game. I for one got super glide from my Ryu Dragon while i was still in Traverse Town on Critical mode and by the second world, i had EXP Walker from Skelter Wild

Take your stuff. If you don't you're gonna be grinding for a loooonnng time. But if you want a super challenge don't take it. Either or.

I don't know why you wouldn't keep your stuff. If I remember correctly critical mode has to be unlocked, so they probably intended for you to keep everything.

Be safe and start a completely new game in the second slot of saved data.